If $x \barwedge y = 6x+y$ and $x \triangleleft y = 3x^{2}-y^{2}$, find $-2 \barwedge (-4 \triangleleft 4)$.
Solution: First, find $-4 \triangleleft 4$ $ -4 \triangleleft 4 = 3(-4)^{2}-4^{2}$ $ \hphantom{-4 \triangleleft 4} = 32$ Now, find $-2 \barwedge 32$ $ -2 \barwedge 32 = (6)(-2)+32$ $ \hphantom{-2 \barwedge 32} = 20$.